Tetrahedron Letters.
Elsevier Ltd.
Vol. 47.
2006.
P. 999-1001

The equation F(x, σ) = 0,x K, in which σ is a parameter and x is an unknown taking values in a given convex cone in a Banach space X, is considered. This equation is examined in a neighborhood of a given solution (x*, σ*) for which the Robinson regularity condition may be violated. Under the assumption that the 2-regularity condition (defined in the paper), which is much weaker than the Robinson regularity condition, is satisfied, an implicit function theorem is obtained for this equation. This result is a generalization of the known implicit function theorems even for the case when the cone K coincides with the entire space X. © MAIK "Nauka/Interperiodica" (Russia), 2006.

Authors

Arutyunov A.V.
^{1}

Number of issue

2

Language

English

Pages

195-205

Status

Published

Link

Volume

46

Year

2006

Organizations

^{1}Peoples Friendship University, ul. Miklukho-Maklaya 6, Moscow, 117198, Russian Federation

Keywords

2-regularity condition; Convex cone; Implicit function theory; Robinson condition

Date of creation

19.10.2018

Date of change

19.10.2018

Share

Tetrahedron Letters.
Elsevier Ltd.
Vol. 47.
2006.
P. 999-1001

Article

Mathematics of Operations Research.
Vol. 31.
2006.
P. 1-12